Optimal control of an age-structured model of HIV infection

Kwon, Hee Dae; Lee, Jeehyun; Yang, Sung

doi:10.1016/j.amc.2012.09.003

Cited by 23 publications

(15 citation statements)

References 24 publications

(45 reference statements)

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“…Since economic resources are limited, epidemiological models have started taking into consideration the economic constraints imposed by limited resources when analyzing control strategies. Optimal control theory has been applied to the mathematical models of HIV models Zarei et al (2010), Kwon et al (2012), Karrakchou et al (2006), Kwon (2007), Roshanfekr et al (2014), , Zhou et al (2014), Adams et al (2005), Costanza et al (2013), Orellana (2011), Malaria Okosun et al (2013, Okosun et al (2011), Okosun and Makinde (2014), Okosun (2011), Kim (2012), Prosper et al (2014), Tuberculosis Moualeu et al (2015), Silva and Torres (2013), Agusto and Adekunle (2014), Bowong and Aziz Alaoui (2013), Whang et al (2011), Vector borne diseases Lashari (2012), Graesboll et al (2014), Sung Lee and Ali Lashari (2014) and other diseases Yan and Zou (2008), Agusto (2013), Brown andJane White (2011), Zaman et al (2008), Okosun and Makinde (2014), Su and Sun (2015), Buonomo et al (2014), Lowden et al (2014), Roshanfekr et al (2014), Apreutesei et al (2014), Imran et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Optimal control in epidemiology

2015

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Mathematical modelling of infectious diseases has shown that combinations of isolation, quarantine, vaccine and treatment are often necessary in order to eliminate most infectious diseases. However, if they are not administered at the right time and in the right amount, the disease elimination will remain a difficult task. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal diseases intervention strategies. The method consists of minimizing the cost of infection or the cost of implementing the control, or both. This paper reviews the available literature on mathematical models that use optimal control theory to deduce the optimal strategies aimed at curtailing the spread of an infectious disease.

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Section: Introductionmentioning

confidence: 99%

Optimal control in epidemiology

2015

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“…For some background of age-structured epidemic models, see the books by Cushing [5] and Webb [41]. By now, lots have been done for age-structured HIV infection models only with cell-free spread (to name a few, see [3,6,8,10,12,21,29,34,38,39]). In spite of this, to the best of our knowledge, only Wang et al [37] studied the following age-structured HIV infection model with both cell-free infection and cell-to-cell transmission,…”

Section: K2k1t0mentioning

confidence: 99%

Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission

Wang¹,

Lang²,

Chen³

2017

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we are concerned with an age-structured HIV infection model incorporating latency and cell-to-cell transmission. The model is a hybrid system consisting of coupled ordinary differential equations and partial differential equations. First, we address the relative compactness and persistence of the solution semi-flow, and the existence of a global attractor. Then, applying the approach of Lyapunov functionals, we establish the global stability of the infection-free equilibrium and the infection equilibrium, which is completely determined by the basic reproduction number.

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“…Due to the priori boundedness of the state and adjoint functions and the resulting Lipschitz structure of the ODEs, the uniqueness of the optimal control is obtained for small t f . The uniqueness of the optimal control follows from the uniqueness of the optimality system, which consists of (16)(17)(18) and (19)(20)(21), (22) with characterizations (23). There is a restriction on the length of the time interval in order to guarantee the uniqueness of the optimality system.…”

Section: Optimal Awareness Programmentioning

confidence: 99%

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

Zakary¹,

Rachik²,

Elmouki³

2016

IJCA

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In this work, a mathematical model for studying the impact of awareness programs on HIV/AIDS outbreak is proposed. The main idea is that people who are susceptible to infection can prevent it, if they are aware how the disease spreads and its consequences, and also the measures to control it. Various forms of communication media, educational, heath institutions and non-governmental organizations play a significant role to promote HIV/AIDS awareness amongst the most concerned people, namely couples and senior secondary school children. The developed HIV model is inspired from the classical SIR epidemic model where a control function is introduced to represent the effectiveness of an awareness program. The obtained optimal control, is characterized in terms of the optimality system, based on Pontryagin's maximum principle, and it is simulated using the Forward-Backward Sweep Method with a progressive-regressive Runge-Kutta fourth order scheme, which is adapted to solve a two-point boundary value problem.

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Optimal control of an age-structured model of HIV infection

Cited by 23 publications

References 24 publications

Optimal control in epidemiology

Optimal control in epidemiology

Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

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